I've read folks write about LME having a strange "funk" to it. Sometimes its described simply as having a "bad" flavor.

I'm not sure how to interpret these descriptions. Would someone care to elaborate on this? Can you provide a more detailed or helpful description? Does this flavor affect only certain kinds of LME (e.g., dark vs. amber vs. light)? Why does this problem not tend to be related to DME? Is it a factor of age, or something else? What is the best way to mitigate the problem (yes, yes, I know you will say All-Grain brewing, but anything apart from that)?

"Extract Twang," as many people call the funk you're talking about, can be caused by several factors.

One cause is if you use old extract. DME tends to have a long shelf life, so this is more common with LME. Make sure the extract you're buying is fresh. If you can't get fresh LME, then stick with DME.

Another cause is scorched wort. Two mistakes many beginning brewers make when starting out with partial boils is: 1) they add all of their extract at the beginning of the boil, which in a partial boil is highly concentrated and susceptible to caramelization. Using late extract additions helps get rid of this issue. And 2) When adding extract to the boil (at any time), they do not remove the pot from the burner. This results in caramelization and scorching of the wort.
Both will cause some undesirable flavors.

Yet another cause is when brewers do not have or use a method to rapidly cool their wort post-boil. My beers improved dramatically once I figured this out.

Finally, many extract recipes (and especially ones designed by newbies) are overloaded with crystal malt. I've seen tons of recipes that call for 1.5 or more pounds of crystal malt, along with their extract. In light extract it's bad enough, because it already has carapils in it. In amber or dark extracts, it's borderline criminal. Then when the beer is cloyingly sweet, they blame the extract. Extract manufacturers list what's in their products. Brewers need to be mindful of that when designing a recipe.

Bear in mind, what I've listed above isn't an indictment of LME. When used properly I think LME produces better tasting beer than DME. It just needs to be handled correctly.

Great answers, folks! But still no one has answered the question of how to identify or describe this "twang" or "funk?" What does it taste like? How can I recognize it on my next batch?

I'm wondering if this is somewhat akin to the issue of "cork taint" in wine. I have drunk wine with a group of connoisseurs and on multiple occasions they would discuss whether the wine was "corked." Despite their best efforts at describing it to me, I was never able to identify it and say: "Ahh, yes, I see what you mean. You're right. It's corked."

I don't know what it is...but I suspect some of the "extract twang" reports are actually off fermentation temperature flavors. Not all but some...

I agree. More often than not, inexperience is the cause of extract twang. Many extract brewers are newbies, and make mistakes. When/if they move to all-grain, they've invested in better equipment while also learning more about the entire brewing/fermentation process. When their all-grain beers come out improved, they blame their flawed extract beers on the extract itself.

It's a shame really. Because while mashing is fun, I find extract brewing to be an enjoyable and rewarding method of brewing. Some of my favorite recipes are extract recipes.

To answer your question, the twang is sort of a bittersweet off flavor, that to me leaves a lasting flavor or mouth feel that is unpleasant. I believe it occurs in LME due to the water present, which probably oxidizes the sugars, making them indigestable to yeast. If you are using LME, make sure to do a full hour boil and remove from the heat source while adding to reduce carmelization.

I have noticed an improvemwnt in my beers since I switched to DME, but I also at the same time improved my fermentation temp with a swamp cooler. I made the switch 3 brews ago and since then they have really been amazing. Im not 100% sure if the DME is superior, but I wont be going back to LME...